## Elementary Particles and the World of Planck Scale

### Manifold, Vacuum Energy, Multiverse, and Eternal Inflation

Research in the early 2000s indicates that the string theory may provide the explanations for "dark energy" and the origin of the "Big Bang". As mentioned earlier, the six extra dimensions curl up into tiny six-dimensional space known as manifold (see Figure 15-21). The equations of string theory specify the arrangement of the manifold configuration, along with their associated branes (green) and lines of force known as flux lines (orange). The physics that is observed in the three large dimensions depends on the size and the structure of the manifold: how many doughnut-like "handles" it has, the length and circumference of each handle, the number and locations of its branes, and the number of flux lines wrapped around each doughnut. The flux through the various donut holes is quantized. This means that it requires only a number of integers to specify. On the Calabi Yau surfaces, the number could be hundreds.

#### Figure 15-21 Manifold [view large image]

Each manifold has an unique potential energy, contributed by fluxes (something similar to magnetic fields), branes and the curvature of the curled-up dimensions. This energy is called the vacuum energy, because it is the energy of the spacetime when the large four dimensions are
completely devoid of matter or fields. The geometry of the small manifold will try to adjust to minimize this energy. As the result, each stable configuration will settle down into the minimum of the vacuum energy as shown by the alphabets in Figure 15-22, where the negative energy is plotted in blue. The diagram depicts a simplified version of only two parameters. Actually, the number of adjustable parameters is enormous. There are solutions with up to about 500 handles and the number of flux lines can be as many as 10. Thus, the number of possible manifold configurations would be around 10500, and each would occupy a stable position in the energy map of multiple parameters. Our universe (see Us in diagram) happens to be one of these with a small cosmological constant (corresponding to the small but positive vacuum energy), which is now driving the observed cosmic acceleration. Large positive vacuum energy will produce too much acceleration, and negative vacuum energy will induce collapse. According to the anthropic principle, we are also living in such a manifold (of the six small dimensions) that the physical laws are suitable for the development of life. A lot of physicists are very uncomfortable with this kind of tautology, which while true, can never be used to create a falsifiable

#### Figure 15-22 Vacuum Energy and Multiverse [view large image]

prediction, and thus cannot be part of scientific reasoning. Actually, it seems to be no worse Newtonian mechanics, which permits an infinite number of orbits around the Sun each one with than different
boundary and initial conditions. The only difference is that the orbits are verifiable; while it is impossible to check out the other vacua in the case of superstring theory. There is one and only one vacuum that we know of.

The possibility of decay from one stable vacuum to another suggests a radical new picture of the universe. Figure 15-23a depicts the large dimension space in color. The blue region represents an universe originally sitting in the minimum vacuum energy A (as shown in Figure 15-22). Decay of a flux line in A creates a different manifold, which tunnels to a new minimum in B (see Figure 15-22 and the red bubble in Figure 15-23a). Then decay of another flux line in B creates another manifold, which tunnels to another new minimum in C (see Figure 15-22 and the green bubble in Figure 15-23a), and so on ad infinitum. The whole universe is therefore a foam of expanding bubbles within bubbles, each with its own laws of physics. Such scenario is referred to as "eternal inflation". Extremely few of the bubbles are suitable for the formation of complex structures such as galaxies and life. The observable universe is a small region within

#### Figure 15-23a Eternal Inflation [view large image]

one of these bubbles as shown in Figure 15-23a. The Big Bang was just the beginning of a new manifold within an older universe.

Another eternal inflation scheme is based on a background space-time "foam" empty of matter and radiation, which experiences local quantum fluctuations in curvature, forming many bubbles of false vacuum that individually inflate into mini-universes with random characteristics. Each universe within the multiverse can have a different set of constants and physical laws.

Recently in 2009, two places within the landscape has been identified for the eternal inflation to take place. The energy density in these places is high enough to create strong gravitational waves. Such waves could have polarized the photons of the cosmic microwave background radiation. The European Space Agency's Planck satellite will look for any polarization to verify the claim.

A superstring theory research in 2007 indicates that there may be a way to arrive at an unique universe without invoking the anthropic principle. It turns out that in spite of previous assumption, the myriad manifolds (ways to compactify the extra dimensions) can transform into each other. As shown in Figure 15-23b there are only a few universes with simple manifold and low Euler number, which is related to the dimensionality and the numbers of holes or handles for the manifold. It is also found that the several manifolds in the sparsely populated tip of the diagram (in Figure 15-23b) seem to correspond to universes like our own. This means that the universe might have started out completely differently and been transformed, through a series of transitions, from one manifold to another, ending up at the tip. Perhaps the universe is minimizing something

#### Figure 15-23b Universes [view large image]

through an unknown mechanism. Further research is required to identify how the more complex universes trickle down to become the one we live in today.

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